BG-MO 2016 Problem 3

For $a,b,c,d>0$ prove that $\frac {a+\sqrt{ab}+\sqrt[3]{abc}+\sqrt[4]{abcd}}{4} \leq \sqrt[4]{a.\frac{a+b}{2}.\frac{a+b+c}{3}.\frac{a+b+c+d}{4}}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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